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p If one takes it that the qualitative diversity and variability of the phenomena of the observable world are not an illusion, then knowledge of observable phenomena implies motion of the substance underlying them. This applies both to continuous substance (the material primary elements of the Ionian philosophers, Aristotle’s matter, Descartes’ matter, the ether and field of classical physics) and discrete substance (the atoms of the ancients, Newton’s hypothetical, absolutely solid particles, Hertz’s material points). The diversity and variation of the observable were explained from the standpoint of antique and classical atomism by the combination of moving ‘indivisibles’ and the dissociation of bodies into primary particles. On the other hand, if bodies consisted of an infinite number of infinitesimal parts, the manifest repetitions and relative constancy of nature would be impossible.

p Motion was thus considered an inalienable property of matter even by the atomistics of antiquity, although it interpreted motion, and matter, in a one-sided way that was later expressed very concretely in the mechanistic views of classical physics.

p The development of classical physics itself, in spite of its additions and innovations, did not change the essence of the ancient atomists’ mechanistic understanding of motion. Newton was an adherent of ancient atomism and, while refining the notion of the particles composing bodies, 232 did not go beyond the framework of the mechanistic idea of motion. The discovery of the law of the conservation of energy and creation of the classical theory of field and statistical physics could, seemingly, have destroyed the notion of invariable particles given once and for all, moving in space, and forming the foundation of the Universe, but the physicists who discovered this law and created the classical theory of field and statistical physics thought differently: the views about matter and motion, which fell within the stream of classical atomism, held by the outstanding physicists of the nineteenth century like Helmholtz, Maxwell, Gibbs, and Boltzmann, who completed the classical period of development of physics, are well known.

p At the same time, it must be acknowledged that this situation could not be avoided; there were not yet sufficient experimental data in classical physics to pose the question of the motion occurring at the very foundation of matter in a new way and in a spirit quite different from the mechanistic tradition. Such data were accumulated much later: the theory of relativity and the development of quantum theory prepared the necessary premises, on the basis of experimental data that no one had even dreamed of in the nineteenth century, for a solution of this physical problem gravitating towards the idea of the reciprocal transformability of elementary particles.

p Philosophy had already, long before, created a doctrine on the development of matter that accords with the experimental data on the transformability of elementary particles. Progressive philosophical thought, which has always fertilised science with seminal ideas (atomistic views; Descartes’ and Lomonosov’s ideas on the conservation of matter and motion; Kant’s cosmogony), is now giving science an understanding of development in its deepest form, free of one-sidedness, in the form of dialectical materialism.

p The two following features of the dialectical understanding of the motion and development of matter must be stressed.

p (1) The motion and development of the world’s phenomena and processes is a struggle of opposites, the division of unity into the mutually exclusive and at the same time reciprocally connected elements. In his fragment ’On the Question of Dialectics’ Lenin defined the splitting of a single 233 whole and the cognition of its contradictory parts as the essence of dialectics.^^1^^ Each contradictory part of the whole develops into its opposite and the opposites pass into one another; in this way a given contradiction is resolved, giving rise to a new phenomenon, a process with a new inherent contradiction. Without unity of opposites there is no evolving phenomenon or process; without the struggle of opposites there is no development or transformation of a given phenomenon into a new one.

p (2) Development, as a unity of opposites, implies that the unity is relative, while the struggle of opposites is absolute.

p The dialectical understanding of the development of phenomena is not compatible either with the subjectivism and relativism that turn the world into a chaos of empty changes, or with the metaphysical outlook in general that immortalises constancy and rest in one way or another.

p Does the dialectical interpretation of development cover the data on the transformability of the elementary particles that, in the notions of modern physics, form the foundation of the matter known to us? All our subsequent exposition will be devoted to this question.

p Let us point out once more that, in accordance with the experimental data of modern physics, reciprocal transformability is an inalienable property of elementary particles. Motion is a mode of existence of matter, motion being not only change of place but also of quality. The experimental data on elementary particles convincingly confirm this very important proposition of dialectical materialism and give it new content.

p Elementary particles like, say, photons, can be engendered during quantum transitions in atoms, accelerated motion of charged particles, and the decay of a pion and certain other particles, or during the annihilation of an electron and a positron, or, in general, of a particle and an antiparticle. They can also be absorbed and ‘disappear’ in interactions with molecules, atoms, and atomic nuclei; they can be scattered by other particles, and can form so-called electronpositron pairs. Photons themselves exist only in motion with the velocity of light; their ‘stopping’ means either their absorption or transformation.

p All other kinds of elementary particles are also capable of being transformed, and are actually transformed into one 234 another in the appropriate conditions; this has been proved in experiment, but we shall not go into the relevant data.² Let us just note two moments relating to the discovery of the law of the universal transformation of elementary particles. (1) This law was partially expressed, in essence, in Dirac’s theory that synthesised quantum and relativistic ideas in regard to the electron. (2) The beginning of its experimental proof was the discovery of the positron (1932), and its completion the discovery of the antiproton (1955). Discovery of the positron led to discovery of the transformation of the electron-positron pair into photons and vice versa. With discovery of the antiproton (and later of the antineutron) the proposition, which was to some extent justified and had a touch of classical atomism in it, that existing heavy particles (the proton, etc.) always remained heavy particles and could not be transformed into lighter ones (and conversely, that light particles always remained light ones) collapsed.

p Reciprocal transformability is inherent in all known elementary particles, the transformations of which are governed by certain conservation laws. The view has been expressed that these laws limit the possibilities of the transformations of elementary particles. This assertion in fact states that these transformations are not a chaos of arbitrary changes but are regular ones governed by law.

p The conservation laws ensure transformations of elementary particles in accordance with their general and specific nature. We are obliged to conclude that the transformations of elementary particles and the conservation in them of certain quantities are two aspects of one and the same phenomenon. The conservation laws (some of which were discovered long before modern physics) reveal what is constant and preserved during transformations of studied objects. If a certain quantity in a physical process remains constant according to such-and-such conservation law, the process itself and the conserved quantity are regarded as something united. Before going more closely into the relationship of conservation and transformability in elementary-particle physics, let us consider this question from the historical aspect.

p The understanding of the variation of bodies according to which the basis of this variation is the combination and dissociation of fundamental, discrete particles, assumes conservation of the number of these particles (only their 235 configuration and relation to one another changes). In correspondence with this understanding, the conservation of matter in its transformations was interpreted ultimately as conservation of the number of these particles, in other words, the development of uncreated, indestructible matter was reduced to the motion (behaviour) of the initial discrete particles.

p This mechanistic interpretation of the development of matter, which prevailed in classical physics, could not in fact be finally exploded by quantum mechanics: it could be assumed that fundamental particles (the kind and number of which do not vary according to the notions of quantum mechanics) moved according to this theory’s laws. The subsequent development of quantum physics (quantum field theory; the theory of elementary particles) finally buried the idea of the ’bricks of matter’; a profound understanding of the development of matter at its very foundations became established in physics, an understanding that is inseparable, on the philosophical plane, from the conception of dialectical materialism.

p The mechanistic understanding of the development of matter led to a mechanistic interpretation of such a fundamental conservation law as the law of the conservation of energy. Helmholtz, who shares credit for the discovery of this law with Mayer and Joule, considered the law of the conservation and transformation of energy in the spirit of mechanism, in particular as proof of the reducibility of all physical processes to mechanical motion. Engels criticised this mechanistic interpretation, pointing to the transformability of the forms of motion as the essence of Mayer’s, Joule’s, and Helmholtz’s discovery, linking the law of the conservation of energy and the law of the conservation of matter together in one law.^^3^^ These ideas of Engels’ have found fruitful application in modern physics.

p The conservation laws that figured in classical physics have been enriched in content and have acquired certain new aspects in contemporary physics, especially in connection with discovery of the reciprocal transformability of elementary particles; conservation laws unknown to classical physics have been discovered. The new element introduced into the interpretation of these laws by modern physics consists in constancy and conservation being regarded in intimate connection with the development of matter, while this 236 development is understood as the transformation of the various forms of matter into one another (contemporary physics provides no grounds for the idea of reducing physical changes to the motion of certain eternal constant elements).

p In modern physics the conservation law asserts that a certain physical quantity remains constant during a physical process. It is important to mention here that immutability and variation are regarded by the conservation law as something united, internally connected with each other; from this angle unchanged quantities remain even during the transformations of fundamental particles (there was no concept of ’particle transformation’, of course, in classical physics), and are used to describe the world of elementary particles.

p This feature of the conservation laws is also reflected in their very content compared with the understanding of them in classical physics. From the standpoint of the latter fundamental laws determine what should or what will necessarily happen to matter; they order the particles that form the basis of the Universe, as it were, to behave in a certain way and not in some other one (the abstract imperative of the Laplacian super intellect dominates the scene).

p The situation is quite different from the angle of modern physical conceptions. The conservation laws limit the possibilities of the transformations of elementary particles; they define which events may and may not occur, and the probabilities of the possible events in the world of fundamental particles. Necessity remains operative in them, but it figures in them not in abstract form but as an actual necessity leading to multiple-valued results and associated with the probabilities of possible events and the conditions of the possibilities being realised.

p In present-day views, elementary particle interactions are governed by the following conservation laws, which can be divided into two groups: (a) exact or rigorous or strict conservation laws, which include the laws of the conservation of energy and momentum, and of angular momentum, the laws of conservation of electric, baryon and lepton charges (these laws are valid for all interactions of elementary particles, strong, electromagnetic, and weak, and are not violated in any of them, which is why they are called rigorous), and (b) conditional or approximate laws which include the laws of conservation of strangeness and parity, the law 237 of conservation of isospin, temporal parity, charge parity, combined parity.

p The development of modern physics indicates that the conservation laws are not absolute in character. Each of them, as is becoming more and more clear, turns out to be valid, not in general, but in certain conditions, determination of the boundaries of which means the cognition of a new stage in the development of matter with the laws inherent to that stage. The conservation laws consequently change as regards their content and form, becoming deeper and more concrete; the class to which they belong also changes.

p Thus, the law of conservation of baryon charge was modified until it took on its present form. This law, which speaks of the impossibility of transformation of the nucleons within an atomic nucleus into leptons and photons, had the following form before the relevant discoveries: in particle transformations the number of protons remains constant before and after interaction; in symbolic form: N_p = const.

p After the discovery of the neutron, antiparticles, and hyperons (and, correspondingly, of their decay reactions) the law of conservation of baryon charge is now written as follows:

p = const,

p where N denotes the number of particles, and the subscripts p, n, A, etc. denote the proton, neutron, various hyperons and, correspondingly, their antiparticles.

p Let us consider another example. The law of the conservation of energy and the law of the conservation of momentum, which existed separately, so to say, in classical physics, were unified in the theory of relativity and enriched in content in the process by acquiring new aspects; they were converted into a broader law than the classical ones. The concepts of energy and momentum were altered correspondingly: they relinquished their ‘classical’ independence and formed two, internally connected aspects of one-and the same essence (expressed mathematically by the concept of a fourdimensional energy-momentum vector). The concept of rest mass, unknown in classical physics (which is important in the theory of elementary particles), emerged; mass and energy accordingly proved to be intimately connected with each other, which led to important theoretical and practical conclusions.

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p The law of conservation of parity is of special interest frorii the angle of these ideas. The quantum concept of parity is inextricably linked with the principle of mirror symmetry, which we shall dwell on later. Before the experiments suggested by Lee and Yang, the law of the conservation of parity was regarded as a strict one. Its violation in weak interactions gave rise to serious difficulties. The ways they were resolved led to Landau’s hypothesis and a new law, thought strict at the time, which was called the law of the conservation of combined parity.

p Anticipating a little, let us make the following assumption: every conservation law at present known as strict can (and in certain circumstances does) turn into an approximate one, but that serves as a prerequisite and reason for the discovery of a new, broader and more concrete strict law, i.e. the difference between the concepts of strict and approximate conservation laws is relative, and these laws are connected by transitions. It cannot be otherwise, since the individual laws discovered by man are various manifestations of the universal law of the conservation of matter and motion.

p The conservation laws governing the transformations of elementary particles express the uncreatability and indestructibility (conservation) of eternally evolving matter at its deepest level at present known. The uncreatability and indestructibility of evolving matter is a necessary condition of its objectivity and reality; therefore, the conservation laws discovered and discoverable by science again and again confirm theobjective reality of the developing world, and science, in turn, in discovering conservation laws, is based on acceptance of its objective reality, i.e. on acceptance of an external world that exists and develops independently of human consciousness.

p Modern physics has not simply connected the ideas of conservation and transformation in regard to the fundamental particles of matter. Its concepts and statements relating to the transformations and interactions of particles clarify the basis of this unity and bring out the reciprocally determining connection between the conservation laws and the so-called symmetry principles. Many types of symmetry were discovered by classical physics (some were known even earlier); they did not, however, play an important role in the understanding of physical phenomena and their laws. In 239 modern physics not only have new types of symmetry not known before been discovered, but, and this is the main point, the close connection between the symmetry principles and conservation laws, and their important role in physical theory, have been clarified. If we approach the symmetry principles of modern physics (and the theory of elementary particles) from the philosophical aspect, the deep truth of Lenin’s words becomes clearly apparent: ’Dialectics in the proper sense is the study of contradiction in the very essence of objects: not only are appearances transitory, mobile, fluid, demarcated only by conventional boundaries, but the essence of things is so as well.’^^4^^

p The symmetries in the theory of elementary particles are precisely ’contradictions in the very essence of objects’ ‘translated’ into the language of modern physics. We shall now take this point up, leaving aside, however, important aspects of the problematics of the symmetry of the laws of physics (in particular, the so-called dynamic or non- geometric symmetries; when physicists, as Wigner put it, ’deal with the dynamic principles of invariance [they] are largely on terra incognita? )^b.

p As we noted above, there is an internal connection between the conservation laws and symmetry principles. A certain symmetry leads to a certain conservation law corresponding to it; such-and-such a conservation law entails a corresponding symmetry, although the link connecting the symmetry and the conservation law is not always simple, and much experimental and theoretical work is required in order to determine the connection between them. The internal relation between the two makes it possible to get a better understanding of the content of the conservation laws and at the same time to determine the great heuristic role of symmetry principles in cognising the laws of nature. Let us consider the philosophical points appertaining to this theme.

p The properties of symmetry in nature Me expressed mathematically by transformations of the space and time coordinates. The equations that express the laws of nature have to be invariant with respect to the corresponding transformations. The invariance of equations expressing the laws of nature or, in short, the invariance of the laws of nature in respect of transformations of one kind or another, also leads to a conservation law of one kind or another.

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p The symmetries and connections between them known to modern physics do not exhaust the wealth of symmetries and connections existing in nature. Let us consider certain most important symmetries.

p Symmetries of classical physics. In classical mechanics there are transformations of translation, shift of time scale, rotation, spatial inversion, temporal inversion, and Galileo’s transformations.

p Transformations reflect symmetries; transformations of spatial inversion, for example, reflect right-left or mirror symmetry; Galileo’s transformations reflect the symmetry of rest and uniform motion in a straight line, and so on. Symmetries lead to conservation laws (the conserved quantities are invariants of the corresponding transformations); invariance of the physical laws with respect to spatial translation, for example, leads to the law of the conservation of momentum, while invariance of the physical laws with respect to shift of the time scale leads to the law of the conservation of energy. In classical physics not all symmetries entail corresponding conservation laws. Thus, the principle of right-left symmetry in classical physics does not lead to a conservation law, but a law corresponding to this symmetry arises in quantum theory: namely, the law of the conservation of parity.

p Symmetries of the theory of relativity. This theory does not simply take over the symmetry principles of classical physics; it introduces new symmetries, or new invariances, corresponding to regularities that cannot manifest themselves within the limits of applicability of classical theories. In that connection the classical principles of symmetry are altered at the appropriate points in the theory of relativity. Thus, the Lorentz transformations reflect not just the symmetry between rest and uniform motion in a straight line (like Galileo’s transformations in classical mechanics), but also, at the same time, a symmetry between space and time that is alien to classical physics. In the theory of relativity physical laws are invariant in respect to transformations of the rotation of the four-dimensional space-time continuum (these transformations can be broken down into transformations of spatial rotation and Lorentz transformations).

p Symmetries of quantum theory. This theory introduces new symmetries corresponding to the microworld 241 regularities discovered by it, about which pre-quantum physics could not have an adequate notion. They are the symmetries of particle and wave, charge symmetry, or the symmetry of particles and antiparticles, and invariance with respect to isotopic spin. The laws of conservation of nuclear and lepton charges, and of strangeness, are manifestations of deep symmetries. Quantum theory also subjected the symmetry principles of pre-quantum physics to profound reconsideration; the new conceptions of right-left symmetry can serve as a striking example of this.

p The discovery of quantum symmetries meant that physics had begun to study the contradictions in the very foundation of matter. In modern physical theory symmetries have acquired great heuristic significance and play a particularly important role in its development. Suffice it to recall that discovery of the symmetry between particle and wave determined, if one can express it so, the main axis of quantum ideas: the laws of quantum mechanics are, of course, invariant with respect to the symmetry between particle and wave, i.e. quantum mechanics reflects this symmetry.

p Of vital interest, however, is approach to the symmetry problem that is becoming more and more defined in modern physics and which, as it seems to us, acquires the total clarity from the philosophical aspect in the light of the dialectical principle of contradiction. In this respect discovery of the breach of the conservation of parity and the interpretation of this violation provide the necessary point of support.

p We shall not go into the physical details associated with the quantum concept of parity. This concept characterises how the wave function describing the state of a micro- particle will change with mirror reflection of the spatial coordinates (coordinates x, y, z being replaced by—x,—y, and —z). The concept of parity makes it possible to express mirror symmetry, or the symmetry between left and right, mathematically, in the form of a conservation law. The fruitfulness of the concept of parity became clear ^luring the development of quantum mechanics, and it was demonstrated that conservation of parity was a consequence of the Schrodinger equation being invariant relative to inversion of left and right. For each state of an atomic system it is possible to determine its ’mirror state’, which is connected with the first one in the same way as any object is connected with its reflection in a mirror.

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p The law of conservation of parity or, correspondingly, the principle of mirror symmetry, operated, it was once thought, in all regions of the macro- and microworlds. The experimental data on weak interactions, however, posed new problems of the principle of mirror symmetry. As Lee and Yang showed, it followed unambiguously from experiments vfiih\K- mesons that the law of conservation of parity did not hold for weak interactions, i.e. instead of symmetry, there was asymmetry between right and left in weak interactions.

p A situation thus developed in which the law of conservation of parity was valid for strong and electromagnetic interactions but ceased to hold for weak interactions. In other words, one had to assume that space was homogeneous and isotropic and at the same time asymmetric with respect to left and right. It did not hold together.

p Among the possible solutions for the difficulties, the greatest philosophical interest attaches to the idea put forward at one time by Landau and independently of him by Lee and Yang.

p In order to consider this idea and the consequences flowing from it that are essential for the problem of symmetry in nature, we must discuss the matter of the symmetry between particles and antiparticles.

p It used to be assumed that there was a substantial asymmetry between positive and negative electricity, which did not manifest itself in electromagnetic phenomena but the basis for which lay in deep laws not yet discovered, pertaining to elementary particles. The first decisive blow to this assumption was struck by the discovery of the positron, which was the direct opposite of the negative electron; now (since the appropriate theoretical research and discovery of the antiproton and other antiparticles) the principle of the symmetry between particles and antiparticles, or the principle of invariance with respect to charge conjugation, has become a leading proposition of the theory of elementary particles.

p It became clear, however, that the situation with the principle of charge symmetry was far from simple and was to some extent similar to that with the principle of mirror symmetry. Beta-decay experiments indicated that, in weak interactions, not only was the law of conservation of parity violated, but also* invariance with respect to charge conjugation, i.e. the principle of symmetry between particles and antiparticles. It could appear that it was necessary to return to 243 the initial idea of the asymmetry of positive and negative electricity, appropriately modified.

p Reality, however, proved to be ‘smarter’. Landau’s idea gave a possibility of a better understanding of symmetry in nature than that existing before it.

p In strong and electromagnetic interactions, as experiment witnesses, the principle of the symmetry between particles and antiparticles and that of symmetry of right and left operate independently of each other, i.e. both charge and parity are conserved. As for weak interactions, Landau assumed that for them the conservation laws did not hold when taken separately, but that a law, called the law of conservation of combined parity, did. This law is as follows: an antiparticle with mirror-symmetrical spatial properties is associated with every particle; the transformation of charge conjugation and of spatial inversion were accordingly unified by Landau in a new transformation that he called combined inversion; physical laws were invariant with respect to combined inversion, i.e. with respect to charge and mirror symmetry simultaneously. Landau’s idea thus excluded mirror asymmetry of space and charge asymmetry of matter; at the same time it did not allow the principles of mirror and charge symmetry to be converted into certain absolutes.

p Landau’s approach thus, in essence, posed the question of the symmetry and invariance of the laws of nature in a quite new way. Those symmetries that had seemed exact, in fact proved to be approximate and relative; at the same time a new exact symmetry was discovered which turned out to represent a novel unity of the old symmetries that had become approximate. One is led to think that the difference between exact and approximate symmetries or, correspondingly, between exact and approximate conservation laws is due to our reflection and is not absolute; approximate and exact symmetries are inseparable, like relative and absolute in dialectics.

p From this angle the concept of symmetry in physics is, so to say, fluid. The different symmetries cease to lead a separate existence; they are bound together by transitions, more and more deeply and completely covering the phenomena and processes of nature, and their essence and laws. The discovery of combined inversion is an important step towards establishing a universal, concrete connection between symmetries in nature. When physics resolves this 244 problem more completely, it will be possible to determine, in particular, why some symmetries have a broader character than others, why such-and-such symmetries exist precisely in certain interactions and not in others, in short, it will provide a chance of identifying the kinds of symmetry more clearly and will lead, in general, to solution of the problem of the relations between, and hierarchy of, symmetries. We shall consider certain details of the problem posed here in the next section.

p On the plane of what has been said, the following point is of philosophical interest: is it possible to arrive at a really unified picture of moving matter that would reflect both the microworld and the vast regions of the Universe?

p Dialectical materialism gives a positive answer to this question. The world is single, and its actual unity consists in its materiality; the world, i.e. moving matter, is cognisable. From these propositions of dialectical materialism there follows the possibility of a picture of the world that reflects ever-evolving matter, and this picture must include knowledge, when such is obtained, of the subatomic and atomic worlds, the macroworld, and the world of cosmic scale, because these worlds are ultimately one and the same world of evolving matter, in spite of their qualitative differences.

p As for inorganic nature, physics has, at one stage or another of its historical development, put forward a fundamental physical theory that was the most mature one for its time and should, it seemed, lead to a unified picture of the then known world. The achievements of classical mechanics, for example, made it possible for the mechanistic picture of the world to emerge in the old physics, in accordance with which the phenomena in nature were reduced to the motions of eternally given particles of matter governed by Newton’s laws. The attempt to understand the world on the basis of classical mechanics proved (as was demonstrated by the theory of relativity and quantum theory) to be a relative truth valid only within certain limits.

p For the same reasons the attempt to construct a unified picture of matter in motion on the basis of classical electromagnetic theory also failed. In our day we face the task of building a single theory of moving matter in terms of the theory of relativity and quantum theory. Let us note the following philosophical aspect of this task, which applies to any scientific picture of the world.

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p A scientific picture of the world is impossible that remains unshakeable not only in its details but also in its main features and does not change with the progress of science. The modern physicist accepts this idea in one way or another; for the dialectical materialist it was clear from the very beginning. We would remind the reader of an idea that has been referred to more than once in our book on the appropriate plane. At the turn of the century, when the electromagnetic picture of the world was established in physics, Lenin wrote, disagreeing with the spiritualist-philosopher James Ward, who ascribed a ‘mechanistic’ picture of the world to materialism: ’It is, of course, sheer nonsense to say that materialism ever maintained ... a “mechanical”, and not an electromagnetic, or some other, immeasurably more complex, picture of the world of moving matter.’^^6^^

p It is this immeasurably more complex picture of the world compared with the mechanistic or electromagnetic picture that is being created in contemporary physics, which could be called a relativistic quantum picture since it is built on the basis of the achievements of both relativistic and quantum physics.

p It is now only being built and is very far from that harmonious whole, from that single, consistently developed picture that the mechanistic picture once was. This is due mainly to there still being no unified relativistic quantum theory of elementary particles free of internal contradictions, but several theories relating to individual types of particle and their interactions (e.g. quantum electrodynamics deals, in spite of the difficulties in it, with questions of the interactions of electrons and positrons with photons; the meson theory, which is not related to quantum electrodynamics, studies the meson-nucleon interaction). Analysis of the difficulties and contradictions of the modern theory of elementary particles would lead us away from our theme. Let us simply stress that the creation of a unifiedjelativistic quantum theory of elementary particles and an associated scientific picture of the world has great progressive significance, because it would mean a new step forward in understanding the material world.

p Among the attempts to create a picture of the world as moving matter in terms of quantum physics, the programme for a unified theory of matter (it is a matter mainly of a programme, since there is as yet no theory that is in any sense 246 complete) suggested by Heisenberg, taking some account of the related work of Dirac, de Broglie, and others, is of great philosophical interest.

p The great plus of this programme compared with the mechanistic and electromagnetic pictures of the world that now belong to the historical past is that it is based on the idea of the reciprocal transformability of all elementary particles rather than on certain constant elements or invariable substance. Since, from this point of view, which rests on experimental material, elementary particles represent a single whole that is internally connected, the foundation of all physical phenomena should contain ’primordial matter’, so to say, a single field whose quanta are elementary particles of all kinds. This field is characterised by the operator spinor wave function, and the elementary particles correspond to combinations of the latter’s base components. It is nonlinear, i.e. its equation reflects the fact that this fundamental field interacts, engendering elementary particles, not with other fields but with itself.

p Heisenberg’s non-linear fundamental field is thus a kind of illustration of Engels’ philosophical remark: ’Spinoza: substance is causa sui strikingly expresses the reciprocal action’.^^7^^

p According to Heisenberg, the equation that describes motion (interaction) of ’primordial matter’ should be invariant with respect to all known transformations with which the theory of elementary particles deals. Having found this equation, Heisenberg obtained information from it about the masses of elementary particles and the elementary electric charge that agreed more or less with their experimental values, and other data about elementary particles.

p In spite of the definite positive results of the theory, mainly qualitative, the attitude of theoretical physicists to it ’fluctuates extraordinarily’, as Tamm put it. Its mathematical basis is recognised as far from satisfactory. In addition the indefinite metric introduced by Heisenberg, and the ’ negative probabilities’ associated with it (they were to help the modern theory of elementary particles get rid of the divergencies, i.e. of infinite values for the mass, charge, and other constants of elementary particles figuring in the theory, instead of the finite values known from experiment), still leave certain essential matters appertaining to this problem obscure, as Tamm has shown. Finally, Bohr’s 247 well-known statement that Heisenberg’s theory is not ’crazy enough’ for a new theory throws into relief the fact that the theory is vulnerable as regards its methodology. In this case Bohr stressed the fact that the ideas of Heisenberg’s theory, like his ’negative probabilities’, are not yet ‘bizarre’ enough to build a really new theory with.

p Heisenberg himself affirmed that the equation he obtained possibly adequately described the law of nature relating to matter. But there was no answer to this question as yet, he continued; it would only be obtained in the future on the basis of more accurate mathematical analysis of the equation and its comparison with the experimental data being accumulated in ever growing quantities.^^8^^

p In our view it is necessary, in creating a unified theory of matter, (1) to take account inter alia of the possibility of a radical revision of ideas about symmetry and invariance in the spirit of the views considered above, and (2) to be guided not only by the methodological principle of explaining the whole by means of its parts, but also by the principle, dialectically connected with it, of explaining the parts by the whole. It is necessary, in particular, to consider the existence of gravitational fields, without which it is hardly possible to construct a really unified theory of matter in the proper sense of the term.

p It must be assumed that such a theory would provide a positive solution of the problem of revising space and time ideas in relation to the scale of elementary particles. The need for such a revision follows not only from general considerations but also from special ones that it would be out of place to discuss here. There is the problem of quantising space and time, i.e. the question of their possibly being discrete. Democritus, for instance, ascribed an atomistic structure equally to space and time as to motion: there existed tiny bits of space and time that were sensibly imperceptible, and also discrete units of motion that could only be comprehended by scientific thought. These ideas of Democritus’ are little known to scientists.

p The conception of abstract, pure discreteness of space, time, and motion, and also the abstract, atomistic interpretation of matter do not accord with the facts; its one- sidedness was overcome during the history of philosophy and science. The dialectical materialist point of view on the problem of the discontinuity and continuity of space and 248 time is briefly expressed in Lenin’s following words: ’ Motion is the essence of space and time. Two fundamental concepts express this essence: (infinite) continuity (Kontinuit&t) and “punctuality” ( = denial of continuity, discontinuit y). Motion is the unity of continuity (of time and space) and discontinuity (of time and space). Motion is a contradiction, a unity of contradictions.’^^9^^

p From the philosophical aspect, the various approaches to resolving the problem of quantising space and time cannot avoid dealing in one way or another with this statement of Lenin’s. Thus Heisenberg postulates a third universal constant (in addition to those already known, i.e. Planck’s constant and the velocity of light)—’fundamental length’ of an order of magnitude of 10 ^^13^^ centimetre (the same order of magnitude as that of the radius of the lightest atomic nucleus), below which present-day quantum field theory is inapplicable, i.e. he postulates a length below which distances are meaningless. He introduced this third universal constant from considerations of dimensionality in an endeavour to overcome difficulties with divergencies.

It is hardly possible to solve the problem of fundamental length in a purely atomistic, formal way. In order to solve this problem, it is necessary, it seems to us, to unite the general theory of relativity and the quantum theory of field, because the problem of quantising (real) space and time cannot be solved outside and independently of that of the discontinuity-continuity of moving matter.